The translation of the physical
properties of textile fibers into textile structures, such as yarns and fabrics
is a function of both the fiber properties and the geometric configuration they
assume in the ultimate end product. Earlier studies of the relationship between
yarn structure and properties have been along empirical or semi-empirical
lines. However, many technologists who are concerned with the evaluation of the
physical properties of textile structures have realized that these
relationships are governed by same physical and engineering concepts as those
e\used so successfully in the characterization of more classic structural
materials such as steel and concrete. Hearle and Backer have given an excellent
account of the progressive development of the ideas in this field of study.
Nevertheless, it is considered appropriate to consider some basic concepts that
are relevant to the study of yarn structure and properties. One such aspect is
the understanding of the geometry of twisted yarns that is so vital in
analyzing the stress-strain behavior of yarns in addition to various other
physical properties.GEOMETRY OF THE IDEALIZED TWISTED YARNS:
In the definition of the geometry
of the single yarn the model is usually adopted as an ideal physical form.
This is a coaxial helix model as illustrated in Fig. 5.5. of Goswami.
The assumptions underlying the model are characterized by the following
assumptions:-
1)
The yarn is circular in cross-section and is uniform
along its length.
2)
It is built-up of a series of superimposed concentric
layers of different radii in each of which the fibers follow a uniform helical
path so that its distance from the centre remains constant.
3)
A filament at the centre will follow the straight line
of the yarn axis, but going out from the centre the helix angle gradually
increases, since the twist per unit length in all the layers remains constant.
4)
The axis of the circular cylinders coincides with the
yarn axis.
5)
The number of filaments of fibers crossing the unit
area is constant throughout the model.
6)
The structure is assumed to be made up of a large
number of filaments: this will avoid any complications arising because of any
discrepancies in packing of fibers. There are two types of packing, I) open
packing where the fibers are in loose position, and ii) close packing
where the fibers are very compact.
The idealized model can be used
to derive some very useful geometrical relations related to its various
physical properties. The parameters involved in characterizing the idealized
geometry are:
R= Yarn radius (cm).
r = Radius of the cylinder containing the helical path of a
particular fiber(cm).
T = Yarn twist, (turns per unit length ( cm ).
h = Length of one turn of twist (cm).
α
= Surface angle of twist (the angle between the axis of a fiber on the surface
and a line
parallel to the
yarn axis (degrees).